Use the diagram and equations below to match the following angles with their correct measures. Given Z = 2b + 6 and Y = 3b - 1. 1. W 130° 2. X 140° 3. Y 40° 4. Z 50°
Accepted Solution
A:
the picture in the attached figure
we know that ∠Y+∠Z=90° ∠Z=2b+6 ∠Y=3b-1 so (2b+6)+(3b-1)=90----> 5b+5=90----> 5b=85----> b=17° ∠Z=2b+6---- 2*17+6-----> ∠Z=40° ∠Y=3b-1---> ∠Y=3*17-1---> ∠Y=50°
angle Y and W are supplementary angles so ∠Y+∠W=180---------> ∠W=180-∠Y------> ∠W=180-50----> ∠W=130°
angle X and Z are supplementary angles so ∠X+∠Z=180---------> ∠X=180-∠Z-----> ∠X=180-40°----> ∠X=140°
the answers are a) ∠Z=40° b) ∠Y=50° c) ∠W=130° d) ∠X=140°